Plots:

Summary plots - For the summary plots, each plot is paired by parameter level vertically and the values in the cells are the mean value across all of the simulations for that parameter level. Sample strategy is on the y-axis and number of sites is on the x-axis.Note that each average encompasses all of the other varying simulation parameters.

Full plots - For the full plots, Each plot represents a unique simulation and the values in the cells are the mean value across all of the 10 iterations of that simulation across all three unique landscape seeds (i.e., all three sets of Neutral Landscape Models) for a total of 30 replicates. Sample strategy is on the y-axis and number of sites is on the x-axis. Since there are a many simulations presented in the full plots, here is a handy key for how the different parameters are laid out within them (H = High, L = Low):

Methods:

K - number of latent factors used in LFMM

TPR - True Positive Rate

FDR - False Discovery Rate

strict vs relaxed TPR/FDR - “relaxed” means any adaptive loci identified was counted as a true positive and “strict” means only an adaptive loci identified with the correct environmental variable was counted as a true positive

pRDA - partial RDA conditioning on two PC axes to control for population genetic structure

lasso vs ridge- “lasso” and “ridge” are different methods utilized by LFMM that have different penalization functions (Caye et al., 2019)

1. LFMM

1.1 Individual sampling

1.1.1 Summary plots

1.1.2 Linear mixed effects models

Only results from the ridge method are used from here on out

Linear mixed effect model
TPR relaxed ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0006 25.3952 25.3952 1 15.3480K 818.2168 2.3 × 10−175*
Population size 0.0702 18.9019 18.9019 1 15.3480K 609.0076 6.8 × 10−132*
Migration 0.2259 195.9239 195.9239 1 15.3480K 6312.5359 0.0*
Selection strength 0.0477 8.7426 8.7426 1 15.3480K 281.6792 1.2 × 10−62*
Spatial autocorrelation 0.2933 330.2319 330.2319 1 15.3480K 10639.8508 0.0*
Environmental correlation −0.0411 6.5014 6.5014 1 15.3480K 209.4718 3.7 × 10−47*
* p < 0.001
Tukey test for TPR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - G −0.0061 0.0040 −1.5222 0.4240951
EG - R 0.0015 0.0040 0.3802 0.9812933
EG - T 0.0270 0.0040 6.7038 1.2 × 10−10
G - R 0.0076 0.0040 1.9024 0.2269527
G - T 0.0331 0.0040 8.2259 4.7 × 10−14
R - T 0.0254 0.0040 6.3235 1.5 × 10−9
Linear mixed effect model
TPR strict ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0006 25.1129 25.1129 1 15.3480K 845.4572 5.5 × 10−181*
Population size 0.0657 16.5584 16.5584 1 15.3480K 557.4577 4.3 × 10−121*
Migration 0.2223 189.6828 189.6828 1 15.3480K 6385.9050 0.0*
Selection strength 0.0433 7.2028 7.2028 1 15.3480K 242.4903 2.9 × 10−54*
Spatial autocorrelation 0.2847 311.2133 311.2133 1 15.3480K 10477.3770 0.0*
Environmental correlation −0.0413 6.5586 6.5586 1 15.3480K 220.8042 1.3 × 10−49*
* p < 0.001
Tukey test for TPR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - G −0.0058 0.0039 −1.4765 0.4517849
EG - R 0.0027 0.0039 0.6968 0.8983321
EG - T 0.0284 0.0039 7.2100 3.4 × 10−12
G - R 0.0085 0.0039 2.1733 0.1306838
G - T 0.0342 0.0039 8.6865 3.3 × 10−14
R - T 0.0256 0.0039 6.5131 4.4 × 10−10
Linear mixed effect model
FDR relaxed ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0027 562.8292 562.8292 1 15.3480K 4655.7420691 0.0*
Population size −0.0120 0.5491 0.5491 1 15.3480K 4.5423554 0.033**
Migration 0.0337 4.3696 4.3696 1 15.3480K 36.1451298 1.9 × 10−9*
Selection strength −0.0110 0.4618 0.4618 1 15.3480K 3.8197220 0.051
Spatial autocorrelation 0.0429 7.0649 7.0649 1 15.3480K 58.4411913 2.2 × 10−14*
Environmental correlation 0.0050 0.0979 0.0979 1 15.3480K 0.8096847 0.370
* p < 0.001
** p < 0.05
Tukey test for FDR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - G −0.0038 0.0079 −0.4735 0.9649227
EG - R −0.0023 0.0079 −0.2838 0.9920304
EG - T −0.0152 0.0079 −1.9180 0.2203753
G - R 0.0015 0.0079 0.1896 0.9975831
G - T −0.0115 0.0079 −1.4445 0.4714650
R - T −0.0130 0.0079 −1.6342 0.3593096
Linear mixed effect model
FDR strict ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0027 548.8420 548.8420 1 15.3480K 4.466024e+03 0.0*
Population size 0.0002 0.0001 0.0001 1 15.3480K 8.464168e-04 0.98
Migration 0.0361 4.9975 4.9975 1 15.3480K 4.066586e+01 1.9 × 10−10*
Selection strength −0.0044 0.0727 0.0727 1 15.3480K 5.913520e-01 0.44
Spatial autocorrelation 0.0631 15.2983 15.2983 1 15.3480K 1.244849e+02 8.5 × 10−29*
Environmental correlation 0.0089 0.3059 0.3059 1 15.3480K 2.488917e+00 0.11
* p < 0.001
Tukey test for FDR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - G −0.0039 0.0080 −0.4874 0.96191968
EG - R −0.0050 0.0080 −0.6255 0.92391572
EG - T −0.0194 0.0080 −2.4217 0.07301793
G - R −0.0011 0.0080 −0.1381 0.99906097
G - T −0.0155 0.0080 −1.9343 0.21363718
R - T −0.0144 0.0080 −1.7962 0.27508272

1.1.3 Full plots

1.2 Site sampling

1.2.1 Summary plots

1.1.2 Linear mixed effects models

Only results from the ridge method are used from here on out

Linear mixed effect model
TPR relaxed ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0044 7.2533 7.2533 1 8.6290K 240.98944 1.3 × 10−53*
Population size 0.0339 2.4888 2.4888 1 8.6290K 82.69083 1.2 × 10−19*
Migration 0.1647 58.5839 58.5839 1 8.6290K 1946.44118 0.0*
Selection strength 0.0134 0.3869 0.3869 1 8.6290K 12.85452 3.4 × 10−4*
Spatial autocorrelation 0.2014 87.5792 87.5792 1 8.6290K 2909.80910 0.0*
Environmental correlation −0.0431 4.0083 4.0083 1 8.6290K 133.17421 1.4 × 10−30*
* p < 0.001
Tukey test for TPR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - EQ 0.0632 0.0046 13.8193 0.0
EG - R 0.0183 0.0046 3.9953 1.9 × 10−4
EQ - R −0.0449 0.0046 −9.8241 3.0 × 10−14
Linear mixed effect model
TPR strict ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0029 3.1039 3.1039 1 8.6290K 114.007196 1.9 × 10−26*
Population size 0.0326 2.2986 2.2986 1 8.6290K 84.426813 4.9 × 10−20*
Migration 0.1656 59.2182 59.2182 1 8.6290K 2175.071475 0.0*
Selection strength 0.0095 0.1932 0.1932 1 8.6290K 7.094369 7.7 × 10−3**
Spatial autocorrelation 0.1973 84.1174 84.1174 1 8.6290K 3089.612423 0.0*
Environmental correlation −0.0410 3.6289 3.6289 1 8.6290K 133.289351 1.3 × 10−30*
* p < 0.001
** p < 0.01
Tukey test for TPR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - EQ 0.0531 0.0043 12.2005 0.0
EG - R 0.0180 0.0043 4.1306 1.1 × 10−4
EQ - R −0.0351 0.0043 −8.0698 4.0 × 10−14
Linear mixed effect model
FDR relaxed ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0128 61.1022 61.1022 1 8.6290K 1669.851792 0.0*
Population size 0.0020 0.0089 0.0089 1 8.6290K 0.244297 0.620
Migration −0.0150 0.4888 0.4888 1 8.6290K 13.357421 2.6 × 10−4*
Selection strength −0.0066 0.0950 0.0950 1 8.6290K 2.595954 0.110
Spatial autocorrelation −0.0226 1.1011 1.1011 1 8.6290K 30.092997 4.2 × 10−8*
Environmental correlation 0.0104 0.2352 0.2352 1 8.6290K 6.427289 0.011**
* p < 0.001
** p < 0.05
Tukey test for FDR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - EQ 0.0298 0.0050 5.9054 1.1 × 10−8
EG - R −0.0066 0.0050 −1.3005 0.3948515
EQ - R −0.0363 0.0050 −7.2060 1.8 × 10−12
Linear mixed effect model
FDR strict ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number −0.0126 59.2899 59.2899 1 8.6290K 1627.843274 0.0*
Population size 0.0026 0.0147 0.0147 1 8.6290K 0.404380 0.52
Migration −0.0132 0.3741 0.3741 1 8.6290K 10.270199 1.4 × 10−3**
Selection strength −0.0060 0.0782 0.0782 1 8.6290K 2.147571 0.14
Spatial autocorrelation −0.0195 0.8244 0.8244 1 8.6290K 22.633321 2.0 × 10−6*
Environmental correlation 0.0111 0.2638 0.2638 1 8.6290K 7.242698 7.1 × 10−3**
* p < 0.001
** p < 0.01
Tukey test for FDR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - EQ 0.0316 0.0050 6.2799 1.0 × 10−9
EG - R −0.0053 0.0050 −1.0619 0.537843
EQ - R −0.0369 0.0050 −7.3417 6.5 × 10−13

1.2.3 Full plots

2. RDA

2.1 Individual sampling

2.1.1 Summary plots

2.1.2 Linear mixed effects models

Only results from the standard RDA (not the partial RDA) are used from here on out

Linear mixed effect model
TPR relaxed ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0006 28.3086 28.3086 1 15.3480K 1288.156605 5.8 × 10−271*
Population size 0.0540 11.2075 11.2075 1 15.3480K 509.986438 4.1 × 10−111*
Migration 0.1518 88.5198 88.5198 1 15.3480K 4028.014106 0.0*
Selection strength 0.0206 1.6345 1.6345 1 15.3480K 74.374525 7.1 × 10−18*
Spatial autocorrelation 0.1446 80.3327 80.3327 1 15.3480K 3655.469294 0.0*
Environmental correlation 0.0075 0.2184 0.2184 1 15.3480K 9.936846 1.6 × 10−3**
* p < 0.001
** p < 0.01
Tukey test for TPR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - G −0.0008 0.0034 −0.2405 0.9951135
EG - R 0.0065 0.0034 1.9156 0.2213617
EG - T 0.0265 0.0034 7.8272 5.3 × 10−14
G - R 0.0073 0.0034 2.1561 0.1356982
G - T 0.0273 0.0034 8.0676 5.5 × 10−14
R - T 0.0200 0.0034 5.9115 2.0 × 10−8
Linear mixed effect model
TPR strict ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0006 24.0305 24.0305 1 15.3480K 1219.2221155 4.1 × 10−257*
Population size 0.0490 9.2314 9.2314 1 15.3480K 468.3687882 2.4 × 10−102*
Migration 0.1408 76.0877 76.0877 1 15.3480K 3860.4223552 0.0*
Selection strength 0.0169 1.0957 1.0957 1 15.3480K 55.5894289 9.4 × 10−14*
Spatial autocorrelation 0.1344 69.4052 69.4052 1 15.3480K 3521.3730590 0.0*
Environmental correlation 0.0022 0.0185 0.0185 1 15.3480K 0.9392982 0.33
* p < 0.001
Tukey test for TPR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - G −0.0012 0.0032 −0.3869 0.98032013
EG - R 0.0065 0.0032 2.0400 0.17334620
EG - T 0.0247 0.0032 7.7174 9.5 × 10−14
G - R 0.0078 0.0032 2.4270 0.07207492
G - T 0.0260 0.0032 8.1043 5.3 × 10−14
R - T 0.0182 0.0032 5.6774 8.2 × 10−8
Linear mixed effect model
FDR relaxed ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0000 0.0368 0.0368 1 15.3480K 10.1028076 1.5 × 10−3*
Population size 0.0013 0.0063 0.0063 1 15.3480K 1.7218093 0.19
Migration 0.0093 0.3323 0.3323 1 15.3480K 91.3286057 1.4 × 10−21**
Selection strength 0.0004 0.0006 0.0006 1 15.3480K 0.1693229 0.68
Spatial autocorrelation −0.0046 0.0808 0.0808 1 15.3480K 22.2004535 2.5 × 10−6**
Environmental correlation −0.0007 0.0018 0.0018 1 15.3480K 0.5071474 0.48
* p < 0.01
** p < 0.001
Tukey test for FDR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - G −0.0014 0.0014 −1.0229 0.7360242
EG - R 0.0017 0.0014 1.2567 0.5906588
EG - T 0.0035 0.0014 2.5777 0.0488592
G - R 0.0031 0.0014 2.2795 0.1027877
G - T 0.0050 0.0014 3.6006 1.8 × 10−3
R - T 0.0018 0.0014 1.3211 0.5494245
Linear mixed effect model
FDR strict ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0001 1.0311 1.0311 1 15.3480K 107.07524 5.2 × 10−25*
Population size 0.0088 0.2966 0.2966 1 15.3480K 30.79914 2.9 × 10−8*
Migration 0.0318 3.8748 3.8748 1 15.3480K 402.38002 2.3 × 10−88*
Selection strength 0.0083 0.2650 0.2650 1 15.3480K 27.51496 1.6 × 10−7*
Spatial autocorrelation 0.0159 0.9737 0.9737 1 15.3480K 101.11404 1.0 × 10−23*
Environmental correlation 0.0092 0.3217 0.3217 1 15.3480K 33.40752 7.6 × 10−9*
* p < 0.001
Tukey test for FDR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - G −0.0002 0.0022 −0.0878 0.9997579
EG - R −0.0001 0.0022 −0.0354 0.9999840
EG - T 0.0044 0.0022 1.9704 0.1992167
G - R 0.0001 0.0022 0.0523 0.9999486
G - T 0.0046 0.0022 2.0582 0.1670032
R - T 0.0045 0.0022 2.0059 0.1857274

1.1.3 Full plots

2.2 Site sampling

2.2.1 Summary plots

2.2.2 Linear mixed effects models

Only results from the standard RDA (not the partial RDA) are used from here on out

Linear mixed effect model
TPR relaxed ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0050 9.1783 9.1783 1 8.6290K 520.09697 7.8 × 10−112*
Population size 0.0651 9.1591 9.1591 1 8.6290K 519.01276 1.3 × 10−111*
Migration 0.1213 31.7970 31.7970 1 8.6290K 1801.80798 0.0*
Selection strength 0.0139 0.4161 0.4161 1 8.6290K 23.57713 1.2 × 10−6*
Spatial autocorrelation 0.1115 26.8304 26.8304 1 8.6290K 1520.37319 1.8 × 10−306*
Environmental correlation 0.0105 0.2383 0.2383 1 8.6290K 13.50409 2.4 × 10−4*
* p < 0.001
Tukey test for TPR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - EQ −0.0055 0.0035 −1.5727 0.2575034
EG - R 0.0161 0.0035 4.6117 1.2 × 10−5
EQ - R 0.0216 0.0035 6.1844 1.9 × 10−9
Linear mixed effect model
TPR strict ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0045 7.6410 7.6410 1 8.6290K 501.596479 4.9 × 10−108*
Population size 0.0572 7.0724 7.0724 1 8.6290K 464.268874 2.4 × 10−100*
Migration 0.1094 25.8482 25.8482 1 8.6290K 1696.809321 0.0*
Selection strength 0.0107 0.2454 0.2454 1 8.6290K 16.106972 6.0 × 10−5*
Spatial autocorrelation 0.1005 21.8210 21.8210 1 8.6290K 1432.446898 3.8 × 10−290*
Environmental correlation 0.0042 0.0388 0.0388 1 8.6290K 2.546423 0.11
* p < 0.001
Tukey test for TPR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - EQ −0.0055 0.0033 −1.6964 0.2065332
EG - R 0.0138 0.0033 4.2405 6.6 × 10−5
EQ - R 0.0193 0.0033 5.9369 8.7 × 10−9
Linear mixed effect model
FDR relaxed ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0001 0.0056 0.0056 1 8.6290K 5.2265766 0.022*
Population size 0.0020 0.0084 0.0084 1 8.6290K 7.7547459 5.4 × 10−3**
Migration 0.0031 0.0211 0.0211 1 8.6290K 19.5612793 9.9 × 10−6***
Selection strength −0.0018 0.0070 0.0070 1 8.6290K 6.5300863 0.011*
Spatial autocorrelation −0.0010 0.0023 0.0023 1 8.6290K 2.1734755 0.140
Environmental correlation 0.0004 0.0003 0.0003 1 8.6290K 0.2523497 0.620
* p < 0.05
** p < 0.01
*** p < 0.001
Tukey test for FDR relaxed
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - EQ 0.0010 0.0009 1.2104 0.4469483
EG - R 0.0007 0.0009 0.8560 0.6680781
EQ - R −0.0003 0.0009 −0.3544 0.9331014
Linear mixed effect model
FDR strict ~ nsamp + sampstrat + K + m + phi + H + r + (1 | seed)
Predictors Fixed Effects Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Sample number 0.0008 0.2183 0.2183 1 8.6310K 23.775616 1.1 × 10−6*
Population size 0.0175 0.6586 0.6586 1 8.6310K 71.717514 2.9 × 10−17*
Migration 0.0314 2.1334 2.1334 1 8.6310K 232.319113 8.8 × 10−52*
Selection strength 0.0030 0.0195 0.0195 1 8.6310K 2.119119 0.15
Spatial autocorrelation 0.0238 1.2223 1.2223 1 8.6310K 133.107697 1.4 × 10−30*
Environmental correlation 0.0132 0.3752 0.3752 1 8.6310K 40.853743 1.7 × 10−10*
* p < 0.001
Tukey test for FDR strict
pairwise ~ sampstrat
Contrast Estimate SE Z ratio p
EG - EQ 0.0035 0.0025 1.4002 0.340779481
EG - R 0.0074 0.0025 2.9149 0.009954792
EQ - R 0.0038 0.0025 1.5148 0.283916857

2.2.3 Full plots